What Does It Mean for k to Be a Square Modulo m?

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k is a square modulo m??

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Homework Statement


This is a portion of the problem. I have to prove that A holds if and only if k is a square modulo m.

I have no idea what "k is a square modulo m" means.

Homework Equations


The Attempt at a Solution


I've looked it up online and found some PDF's on cryptography.l
My best guess is that "k is a square modulo m" means x^{2} \equiv k \: (mod\:m) has a solution x.

Is that right?
 
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stgermaine said:
\:

Homework Statement


This is a portion of the problem. I have to prove that A holds if and only if k is a square modulo m.

I have no idea what "k is a square modulo m" means.

Homework Equations





The Attempt at a Solution


I've looked it up online and found some PDF's on cryptography.l
My best guess is that "k is a square modulo m" means x^{2} \equiv k \: (mod\:m) has a solution x.

Is that right?

Yes, that's what it means.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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